Topological superconductivity as an exotic quantum phenomenon with coupled nontrivial topological order and superconductivity together in a single substance has drawn extensive attention because of its novelty as well as the potential for quantum computation[1]}, [2]}, [3]}, [4]}, [5]}, [6]}. A direct idea for producing topological superconductors is to create superconductivity based on the well recognized topological insulators[7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}. The topological insulating states in highly efficient thermoelectric materials Bi\(_2\) Te\(_3\)  and Bi\(_2\) Se\(_3\)  and their alloy Bi\(_{2}\) Te\(_{3-x}\) Se\(_{x}\)  have been established from angle-resolved photoemission[15]}, [16]}, [17]} and transport[18]} experiments. Superconductivity was also observed based on these popular topological insulators by the application of pressure[19]}, [20]}, [21]}, chemical dopant[22]}, and heterostructures[23]}, [24]}. However, the experiments mainly focusing on Bi\(_{2}\) Se\(_3\)  doped by metals such as Cu[25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, Sr[36]}, [37]}, [38]}, [39]}, and Nb[40]}, [41]}, [42]}, [43]}, [44]}, [45]}, [46]} have not provided the consistent evidence to support the topological superconductivity.
Here we carry out a systematic high-pressure study on a topological insulator Bi\(_{2}\) Te\(_{2.7}\) Se\(_{0.3}\)  to provide the convincing evidence for the expected topological superconductivity. Four phases with different structures are found upon compression by the X-ray diffraction, Raman scattering, and electrical transport measurements. The Hall resistivity and electronic structure calculations help to identify the topological surface state in the entire initial phase, while superconductivity is found to coexist with such a state of the compressed material after its passing the electronic topological transition, followed by three other superconducting phases without topological character. For these superconducting phases, we observe that the upper critical field follows with the temperature in the critical exponent \({2/3}\)  for the first one with the topological surface state and 1 for the left. These observations support the realization of the topological superconductivity in the initial phase according to the theoretically proposed critical field measure.
Therefore, this work points out a big pool and new direction for finding topological superconductors from topological thermoelectric materials. The results also demonstrate that the critical field measure is an easy and powerful method for the identification of topological superconductivity in the system where topological surface states and superconductivity coexist.
